DG-enhanced Hecke and KLR algebras - Archive ouverte HAL
Article Dans Une Revue Symmetry, Integrability and Geometry : Methods and Applications Année : 2023

DG-enhanced Hecke and KLR algebras

Résumé

We construct DG-enhanced versions of the degenerate affine Hecke algebra and of the affine Hecke algebra. We extend Brundan-Kleshchev and Rouquier's isomorphism and prove that after completion DG-enhanced versions of affine Hecke algebras (degenerate or nondegenerate) are isomorphic to completed DG-enhanced versions of KLR algebras for suitably defined quivers. As a byproduct, we deduce that these DG-algebras have homologies concentrated in degree zero. These homologies are isomorphic respectively to the degenerate cyclotomic Hecke algebra and the cyclotomic Hecke algebra.
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Dates et versions

hal-02163765 , version 1 (25-09-2019)
hal-02163765 , version 2 (23-11-2023)

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Domaine public

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Ruslan Maksimau, Pedro Vaz. DG-enhanced Hecke and KLR algebras. Symmetry, Integrability and Geometry : Methods and Applications, 2023, 19 (095), ⟨10.3842/SIGMA.2023.095⟩. ⟨hal-02163765v2⟩
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